Is there any way possible to tail a falling star or comet-like particle?
For the particles:

Start with a sphere
move one vertex far away using proportional editing  so that neighbor vertices are also stretched proportionally

to create the cloud of particles, use 2 array modifiers to create a matrix, apply the modifiers and separate by loose parts


use proportional editing with Random and smooth fall off in order to arrange the particles. Alternatively, use Randomize Tranform.

create a gradient based shader, use Color Ramps to control color, emission and transparency fall offs (don't forget to turn Alpha Blend mode for transparency to work)


For the background:
Create a world shader based on spherical or linear gradient. Use the Vector Mapping scale, position and rotations to control gradient position in the sky.

For animation: Here is the same object used in a particle system (added plane emitter and moved camera around):